ORIGINAL ARTICLE European Journal of Applied Physics www.ej-physics.org On the Mechanism of Atmospheric Vortex Formation and How to Weaken a Tornado Andrei Nechayev and Alexander Solovyev ABSTRACT Published Online: December 25, 2019 A hydrodynamic mechanism of tornado formation is proposed: it is based on the air density decrease in ascending jets. The empirical verification of this mechanism DOI :10.24018/2019.1.1.1 is considered. The ways are discussed to weaken the tornado by reducing the A. M. Nechayev* inflow streams humidity or by introducing the discontinuity of air jets connecting Lomonosov’s Moscow State University, the lower and upper layers of the atmosphere. Geographic Department, Russia. (e-mail: and.nechayev@ gmail.com) Keywords: atmospheric vortex, hurricane, waterspout, tornado A. A. Solovyev Lomonosov’s Moscow State University, Geographic Department, Russia. (e-mail: [email protected]) *Corresponding Author The atmospheric vortex, as a natural phenomenon, has long 3. The intensification of the vortex is accompanied by an been known. Its most formidable varieties - such as tornadoes acceleration of air rotation and a drop in pressure in the and hurricanes - are too familiar to many inhabitants of our center; planet, as they bring them troubles and troubles. Modern 4. The origin of a natural vortex can occur in a relatively methods of photo and video fixation contain colossal calm atmosphere. information about atmospheric vortices from the tiny and 5. An atmospheric vortex is formed in the Earth’s harmless dust "devils" to deadly tornadoes that destroy atmosphere, which is barotropic: the air density in it depends everything in their path, and hurricanes that flood vast on pressure and usually decreases with height. territories with rain. A lot of scientific work in the field of In this paper, we will develop the new hydrodynamic meteorology and atmospheric physics is devoted to vortices, mechanism proposed in [6] in order to analyze certain the empirical laws of their behavior are quite well established hydrodynamic factors that can lead to the formation of stable and described [1]. As for theoretical works, the most cited zones of reduced pressure in the earth's atmosphere, inside ones [2-4] liken the atmospheric vortex to the Carnot heat and around which an upward air movement occurs. The engine, deriving the condition for its formation from essence of this mechanism is as follows. thermodynamic relations and the integral laws of Imagine a pipe with expansion and a fluid flowing conservation of energy, mass, angular momentum. through the pipe, which, in the place of expansion, changes Meanwhile, the atmospheric vortex is a fundamentally open its density from r to r : rr< . The expansion is chosen hydrodynamic system, to which conservation laws are not 1 2 21 always applicable. In any case, the physically clear and in a special way so as to ensure the constancy of the speed v simple mechanism of atmospheric vortex formation, based on the condition of mass conservation rvS= const unfortunately, is absent. where S is the pipe section. Thus, the cross section of the In [5] it was demonstrated that many of the so-called pipe "tracks" the density of the fluid, keeping the flow rate hydrodynamic “paradoxes” can have a simple explanation in constant, since rS= const . the framework of classical hydrodynamics, if its laws are Let us write the Bernoulli equation for one-dimensional used correctly. Here we will try to use a similar approach to fluid flow along a streamline with a coordinate s . Let us explain the observed atmospheric phenomenon, which is still proceed from the generalized form of Newton's second law mysterious. The desire to find and understand a certain for a fluid with variable density (in the absence of mass “universal” mechanism for the formation of an atmospheric forces): vortex grows stronger when it becomes obvious that almost Dv()r ¶ p all natural vortices, regardless of their scale, have many =--Fv(), (1) common properties. The main ones are as follows: Dt¶ s fr 1. The lower part of the axis of the atmospheric vortex, where p is the pressure inside the fluid, v is the linear around which the air rotates, is always at a minimum of velocity ( vst=¶¶/ ), F is the friction force acting on the atmospheric pressure; fr 2. Air in a vortex moves in an ascending spiral, from fluid particle. The pressure at the ends of the pipe and p0 p2 bottom to top; is kept constant. Going to the stationary state ( ¶¶()/rvt), we can write: DOI: http://dx.doi.org/10.24018/ejphysics.2019.1.1.1 Vol 1 | Issue 1 | December 2019 1 ORIGINAL ARTICLE European Journal of Applied Physics www.ej-physics.org ¶¶()rvp light gas with a density many times lower than the density of (2) vFv=-- fr () the surrounding air. This happens, for example, in the case of ¶¶ss stratospheric balloon filled with helium. Actually convective In the first section L where , the pressure drops from rise of hot air has a relatively low speed, as it is easy to notice 1 rr= 1 when observing the flames of a fire (temperature above 1000 p to p , and the speed increases from 0 to v, integration 0 1 C) or ordinary water vapor (temperature 100 C) rising above (2) gives the standard Bernoulli equation with friction: a boiling pan. Obviously, a mechanism other than thermal 2 convection acts in the free atmosphere, which creates in the r1v (3) ()pp01-= + FLfr1 1 lower and middle layers of the troposphere quite intense and 2 long-lived zones of air rise with speeds exceeding units and Integrating (2) over a segment of length L where the even tens of meters per second. These zones are well known 2 density decreases and the speed remains constant, we have: to passengers of airliners falling into air holes, parachutists 2 and gliders who are near the base of a thundercloud, tourists ()()pp-=rrn-+ FvLfr 2 () (4) 12 21 2 and climbers on the slopes of mountain peaks. In all these Thus, for a fluid flow with a variable density, one can expect cases, there are practically no noticeable temperature the appearance of a zone of reduced pressure in those places differences. Therefore, the mechanism of lifting air should be where the density begins to decrease. This pressure drop is due to hydrodynamic reasons. greater, the greater the difference in densities and the velocity There is an obvious, but not always recognized feature of the fluid. Friction weakens this effect. From (4) it follows of the behavior of the volumes of air inside the atmosphere. that there will be no pressure drop ( pp³ ) if the friction The weight of these volumes is balanced by buoyancy, and 12 when the temperatures are equal, they are in indifferent in the second section is sufficiently large. If we neglect the equilibrium. Prandtl in his famous work [7] wrote about the friction forces (which is permissible for air), then it can be excess pressure arising in a liquid as a result of its motion. shown that the described system has instability with positive This pressure "... is distributed in the liquid as if it was feedback between the flow velocity and the pressure drop. weightless and had only an inert mass ... Each particle of a Indeed, summing (3) and (4) and neglecting friction, we heavy liquid hangs in a stream under the action of the obtain equation (5) for the flow velocity at the point where supporting forces of the surrounding particles." Any, the the density begins to decrease: slightest, force applied to the volume in the vertical direction r 2 (no matter up or down) sets it in motion just as if this force pp-=()r -1 v (5) 02 22 was applied horizontally. The gravitational force is balanced From this equation it follows that velocity tends to infinity by a vertical gradient of hydrostatic pressure, and a balloon when the density decreases by half. However, this filled with room air moves equally easily both to the side and “catastrophe” will not happen if we take into account friction to the ceiling. factors in (3) and (4). The velocity will not increase Therefore, considering the movement of air directed vertically upwards, we can “forget” about the weight of the indefinitely, and the pressure p will not drop to zero. The 1 air, since it is compensated by the Archimedean force, and frictional forces, which we neglected for clarity, prevent this. assume that the initial pressure at all altitudes is Indeed, the friction forces increase with velocity “conditionally” the same and equal to some reference Ffr pressure . And the beginning of the movement is caused increasing and, as follows from (4), friction in the second p section will reduce the pressure drop, which should stabilize by primary overpressure. It is important for us that there is a certain force that can make air move upward, to an area the situation. The knowledge of the dependences Fv() fr where the air density is much less. The source of such a force allows one to solve equations (3) and (4) and obtain an can be the inhibition of air flow due to various reasons. When unambiguous value of the flow velocity v and pressure p the flow velocity decreases to zero in the zone of collision 1 with a fixed surface at the so-called critical point [5], the at given values rr, . The described instability mechanism 12 pressure increases by an amount rv2 /2. This overpressure is fundamental, since a decrease in the momentum rv due either stops the flow or causes it to change direction in to a decrease in density must be compensated by the pressure accordance with the surrounding conditions.